Question:

A deferred annuity policy is sold to a life aged 45 with the following benefits:

• Basic payments start at $30,000 from age 65, increasing by $2,000 each year;
• If the policyholder dies before age 65, all premiums paid will be refunded without interest immediately on death.

Level premiums are payable annually in advance from age 45 until age 65 or earlier death.

(a) Show that the annual gross premium for this policy is $18,428.47.

(b) Calculate the retrospective gross premium reserve at age 60.

(c) Verify your answer in (b) by the prospective policy value.

Expenses: Initial cost of $1,000 plus 0.6% of each annuity payment and 1% of each premium on collection

Basis: AM92 Ultimate mortality, 4% pa interest